Gongjie Li

Eccentricity growth and orbit flip in near-coplanar hierarchical three-body systems

The secular dynamical evolution of a hierarchical three-body system in which a distant third object orbits around a binary has been studied extensively, demonstrating that the inner orbit can undergo large eccentricity and inclination oscillations. It was shown before that starting with a circular inner orbit, large mutual inclination (40°-140°) can produce long timescale modulations that drive the eccentricity to extremely large values and can flip the orbit. Here, we demonstrate that starting with an almost coplanar configuration, for eccentric inner and outer orbits, the eccentricity of the inner orbit can still be excited to high values, and the orbit can flip by ~180°, rolling over its major axis. The ~180° flip criterion and the flip timescale are described by simple analytic expressions that depend on the initial orbital parameters. With tidal dissipation, this mechanism can produce counter-orbiting exoplanetary systems. In addition, we also show that this mechanism has the potential to enhance the tidal disruption or collision rates for different systems. Furthermore, we explore the entire e 1 and i 0 parameter space that can produce flips.

Chaos in the test particle eccentric Kozai-Lidov mechanism

The Kozai-Lidov mechanism can be applied to a vast variety of astrophysical systems involving hierarchical three-body systems. Here, we study the Kozai-Lidov mechanism systematically in the test particle limit at the octupole level of approximation. We investigate the chaotic and quasiperiodic orbital evolution by studying surfaces of section and the Lyapunov exponents. We find that the resonances introduced by the octupole level of approximation cause orbits to flip from prograde to retrograde and back as well as cause significant eccentricity excitation, and the chaotic behaviors occur when the mutual inclination between the inner and the outer binary is high. We characterize the parameter space that allows large amplitude oscillations in eccentricity and inclination.

ARE TIDAL EFFECTS RESPONSIBLE FOR EXOPLANETARY SPIN–ORBIT ALIGNMENT?

The obliquities of planet-hosting stars are clues about the formation of planetary systems. Previous observations led to the hypothesis that for close-in giant planets, spin-orbit alignment is enforced by tidal interactions. Here, we examine two problems with this hypothesis. First, Mazeh and coworkers recently used a new technique -- based on the amplitude of starspot-induced photometric variability -- to conclude that spin-orbit alignment is common even for relatively long-period planets, which would not be expected if tides were responsible. We re-examine the data and find a statistically significant correlation between photometric variability and planetary orbital period that is qualitatively consistent with tidal interactions. However it is still difficult to explain quantitatively, as it would require tides to be effective for periods as long as tens of days. Second, Rogers and Lin argued against a particular theory for tidal re-alignment by showing that initially retrograde systems would fail to be re-aligned, in contradiction with the observed prevalence of prograde systems. We investigate a simple model that overcomes this problem by taking into account the dissipation of inertial waves and the equilibrium tide, as well as magnetic braking. We identify a region of parameter space where re-alignment can be achieved, but it only works for close-in giant planets, and requires some fine tuning. Thus, while we find both problems to be more nuanced than they first appeared, the tidal model still has serious shortcomings.

INTERACTION CROSS SECTIONS and SURVIVAL RATES for PROPOSED SOLAR SYSTEM MEMBER PLANET NINE

Motivated by the report of a possible new planetary member of the Solar System, this work calculates cross sections for interactions between passing stars and this proposed Planet Nine. Evidence for the new planet is provided by the orbital alignment of Kuiper Belt objects, and other Solar System properties, which suggest a Neptune-mass object on an eccentric orbit with semimajor axis

On the Spin-axis Dynamics of a Moonless Earth

a_9\approx400-1500

Accumulated tidal heating of stars over multiple pericentre passages near SgrA

AU. With such a wide orbit, Planet Nine has a large interaction cross section, and is susceptible to disruption by passing stars. Using a large ensemble of numerical simulations (several million), and Monte Carlo sampling, we calculate the cross sections for different classes of orbit-altering events: [A] scattering the planet into its proposed orbit from a smaller orbit, [B] ejecting it from the Solar System from its current orbit, [C] capturing the planet from another system, and [D] capturing a free-floating planet. Results are presented for a range of orbital elements with planetary mass

UNCOVERING CIRCUMBINARY PLANETARY ARCHITECTURAL PROPERTIES FROM SELECTION BIASES

m_9=10M_{earth}

DEVIATION OF STELLAR ORBITS FROM TEST PARTICLE TRAJECTORIES AROUND SGr A* DUE TO TIDES AND WINDS

. Removing Planet Nine from the Solar System is the most likely outcome. Specifically, we obtain ejection cross sections

The Eccentric Kozai–Lidov Mechanism for Outer Test Particle

\sigma_{int}\sim5\times10^6

DYNAMICAL CONSIDERATIONS FOR LIFE IN MULTI-HABITABLE PLANETARY SYSTEMS

AU